Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4851,2,Mod(1,4851)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4851, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4851.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4851 = 3^{2} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4851.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(38.7354300205\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.837.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.52892\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4851.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.52892 | −1.78822 | −0.894108 | − | 0.447852i | \(-0.852189\pi\) | ||||
−0.894108 | + | 0.447852i | \(0.852189\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.39543 | 2.19771 | ||||||||
\(5\) | 0.133492 | 0.0596994 | 0.0298497 | − | 0.999554i | \(-0.490497\pi\) | ||||
0.0298497 | + | 0.999554i | \(0.490497\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −6.05784 | −2.14177 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.337590 | −0.106755 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.133492 | −0.0370240 | −0.0185120 | − | 0.999829i | \(-0.505893\pi\) | ||||
−0.0185120 | + | 0.999829i | \(0.505893\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.52892 | 1.63223 | ||||||||
\(17\) | −5.05784 | −1.22671 | −0.613353 | − | 0.789809i | \(-0.710180\pi\) | ||||
−0.613353 | + | 0.789809i | \(0.710180\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.924344 | 0.212059 | 0.106030 | − | 0.994363i | \(-0.466186\pi\) | ||||
0.106030 | + | 0.994363i | \(0.466186\pi\) | |||||||
\(20\) | 0.586754 | 0.131202 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.52892 | 0.539167 | ||||||||
\(23\) | 7.05784 | 1.47166 | 0.735830 | − | 0.677166i | \(-0.236792\pi\) | ||||
0.735830 | + | 0.677166i | \(0.236792\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.98218 | −0.996436 | ||||||||
\(26\) | 0.337590 | 0.0662069 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.86651 | −0.717993 | −0.358996 | − | 0.933339i | \(-0.616881\pi\) | ||||
−0.358996 | + | 0.933339i | \(0.616881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.79085 | −0.501252 | −0.250626 | − | 0.968084i | \(-0.580636\pi\) | ||||
−0.250626 | + | 0.968084i | \(0.580636\pi\) | |||||||
\(32\) | −4.39543 | −0.777009 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.7909 | 2.19361 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.98218 | 1.64106 | 0.820530 | − | 0.571603i | \(-0.193678\pi\) | ||||
0.820530 | + | 0.571603i | \(0.193678\pi\) | |||||||
\(38\) | −2.33759 | −0.379207 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.808672 | −0.127862 | ||||||||
\(41\) | 11.8487 | 1.85045 | 0.925227 | − | 0.379414i | \(-0.123874\pi\) | ||||
0.925227 | + | 0.379414i | \(0.123874\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.05784 | −0.466316 | −0.233158 | − | 0.972439i | \(-0.574906\pi\) | ||||
−0.233158 | + | 0.972439i | \(0.574906\pi\) | |||||||
\(44\) | −4.39543 | −0.662635 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −17.8487 | −2.63165 | ||||||||
\(47\) | −3.07566 | −0.448631 | −0.224315 | − | 0.974517i | \(-0.572015\pi\) | ||||
−0.224315 | + | 0.974517i | \(0.572015\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 12.5995 | 1.78184 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.586754 | −0.0813681 | ||||||||
\(53\) | 4.79085 | 0.658074 | 0.329037 | − | 0.944317i | \(-0.393276\pi\) | ||||
0.329037 | + | 0.944317i | \(0.393276\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.133492 | −0.0180000 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.77808 | 1.28393 | ||||||||
\(59\) | −12.6574 | −1.64785 | −0.823924 | − | 0.566700i | \(-0.808220\pi\) | ||||
−0.823924 | + | 0.566700i | \(0.808220\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 7.05784 | 0.896346 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.94216 | −0.242771 | ||||||||
\(65\) | −0.0178201 | −0.00221031 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.92434 | 1.09028 | 0.545141 | − | 0.838344i | \(-0.316476\pi\) | ||||
0.545141 | + | 0.838344i | \(0.316476\pi\) | |||||||
\(68\) | −22.2313 | −2.69595 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.11567 | 0.725797 | 0.362898 | − | 0.931829i | \(-0.381787\pi\) | ||||
0.362898 | + | 0.931829i | \(0.381787\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.86651 | −0.920705 | −0.460353 | − | 0.887736i | \(-0.652277\pi\) | ||||
−0.460353 | + | 0.887736i | \(0.652277\pi\) | |||||||
\(74\) | −25.2441 | −2.93457 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.06289 | 0.466045 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.1157 | 1.58814 | 0.794069 | − | 0.607828i | \(-0.207959\pi\) | ||||
0.794069 | + | 0.607828i | \(0.207959\pi\) | |||||||
\(80\) | 0.871558 | 0.0974431 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −29.9644 | −3.30901 | ||||||||
\(83\) | −1.20915 | −0.132721 | −0.0663606 | − | 0.997796i | \(-0.521139\pi\) | ||||
−0.0663606 | + | 0.997796i | \(0.521139\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.675180 | −0.0732336 | ||||||||
\(86\) | 7.73302 | 0.833873 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.05784 | 0.645767 | ||||||||
\(89\) | 15.5817 | 1.65166 | 0.825829 | − | 0.563921i | \(-0.190708\pi\) | ||||
0.825829 | + | 0.563921i | \(0.190708\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 31.0222 | 3.23429 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.77808 | 0.802248 | ||||||||
\(95\) | 0.123392 | 0.0126598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.7909 | −1.29871 | −0.649357 | − | 0.760484i | \(-0.724962\pi\) | ||||
−0.649357 | + | 0.760484i | \(0.724962\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −21.8988 | −2.18988 | ||||||||
\(101\) | −9.59180 | −0.954420 | −0.477210 | − | 0.878789i | \(-0.658352\pi\) | ||||
−0.477210 | + | 0.878789i | \(0.658352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.84869 | −0.970420 | −0.485210 | − | 0.874398i | \(-0.661257\pi\) | ||||
−0.485210 | + | 0.874398i | \(0.661257\pi\) | |||||||
\(104\) | 0.808672 | 0.0792968 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.1157 | −1.17678 | ||||||||
\(107\) | −0.924344 | −0.0893597 | −0.0446799 | − | 0.999001i | \(-0.514227\pi\) | ||||
−0.0446799 | + | 0.999001i | \(0.514227\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.52387 | −0.816439 | −0.408219 | − | 0.912884i | \(-0.633850\pi\) | ||||
−0.408219 | + | 0.912884i | \(0.633850\pi\) | |||||||
\(110\) | 0.337590 | 0.0321880 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.1157 | 1.13975 | 0.569873 | − | 0.821733i | \(-0.306992\pi\) | ||||
0.569873 | + | 0.821733i | \(0.306992\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.942164 | 0.0878573 | ||||||||
\(116\) | −16.9950 | −1.57794 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 32.0094 | 2.94671 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 15.1735 | 1.37374 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.2670 | −1.10161 | ||||||||
\(125\) | −1.33254 | −0.119186 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.90652 | −0.790326 | −0.395163 | − | 0.918611i | \(-0.629312\pi\) | ||||
−0.395163 | + | 0.918611i | \(0.629312\pi\) | |||||||
\(128\) | 13.7024 | 1.21113 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.0450656 | 0.00395251 | ||||||||
\(131\) | −15.6974 | −1.37149 | −0.685743 | − | 0.727844i | \(-0.740523\pi\) | ||||
−0.685743 | + | 0.727844i | \(0.740523\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −22.5689 | −1.94966 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 30.6395 | 2.62732 | ||||||||
\(137\) | −14.6395 | −1.25074 | −0.625370 | − | 0.780328i | \(-0.715052\pi\) | ||||
−0.625370 | + | 0.780328i | \(0.715052\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.6496 | −1.58184 | −0.790921 | − | 0.611918i | \(-0.790398\pi\) | ||||
−0.790921 | + | 0.611918i | \(0.790398\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.4660 | −1.29788 | ||||||||
\(143\) | 0.133492 | 0.0111632 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.516148 | −0.0428637 | ||||||||
\(146\) | 19.8938 | 1.64642 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 43.8759 | 3.60658 | ||||||||
\(149\) | −11.8665 | −0.972142 | −0.486071 | − | 0.873919i | \(-0.661570\pi\) | ||||
−0.486071 | + | 0.873919i | \(0.661570\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.3248 | −0.921601 | −0.460800 | − | 0.887504i | \(-0.652438\pi\) | ||||
−0.460800 | + | 0.887504i | \(0.652438\pi\) | |||||||
\(152\) | −5.59952 | −0.454181 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.372556 | −0.0299244 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.3827 | 1.62671 | 0.813357 | − | 0.581766i | \(-0.197638\pi\) | ||||
0.813357 | + | 0.581766i | \(0.197638\pi\) | |||||||
\(158\) | −35.6974 | −2.83993 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.586754 | −0.0463870 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.3070 | −1.51224 | −0.756120 | − | 0.654432i | \(-0.772908\pi\) | ||||
−0.756120 | + | 0.654432i | \(0.772908\pi\) | |||||||
\(164\) | 52.0800 | 4.06677 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.05784 | 0.237334 | ||||||||
\(167\) | 12.6395 | 0.978077 | 0.489038 | − | 0.872262i | \(-0.337348\pi\) | ||||
0.489038 | + | 0.872262i | \(0.337348\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9822 | −0.998629 | ||||||||
\(170\) | 1.70748 | 0.130957 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.4405 | −1.02483 | ||||||||
\(173\) | −19.8487 | −1.50907 | −0.754534 | − | 0.656261i | \(-0.772137\pi\) | ||||
−0.754534 | + | 0.656261i | \(0.772137\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.52892 | −0.492136 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −39.4049 | −2.95352 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.67518 | −0.198845 | −0.0994223 | − | 0.995045i | \(-0.531699\pi\) | ||||
−0.0994223 | + | 0.995045i | \(0.531699\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −42.7552 | −3.15196 | ||||||||
\(185\) | 1.33254 | 0.0979703 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.05784 | 0.369866 | ||||||||
\(188\) | −13.5188 | −0.985961 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.312049 | −0.0226384 | ||||||||
\(191\) | −3.32482 | −0.240576 | −0.120288 | − | 0.992739i | \(-0.538382\pi\) | ||||
−0.120288 | + | 0.992739i | \(0.538382\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.3726 | 1.32249 | 0.661243 | − | 0.750172i | \(-0.270029\pi\) | ||||
0.661243 | + | 0.750172i | \(0.270029\pi\) | |||||||
\(194\) | 32.3470 | 2.32238 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.11567 | 0.578218 | 0.289109 | − | 0.957296i | \(-0.406641\pi\) | ||||
0.289109 | + | 0.957296i | \(0.406641\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.52387 | 0.462465 | 0.231232 | − | 0.972899i | \(-0.425724\pi\) | ||||
0.231232 | + | 0.972899i | \(0.425724\pi\) | |||||||
\(200\) | 30.1812 | 2.13414 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24.2569 | 1.70671 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.58170 | 0.110471 | ||||||||
\(206\) | 24.9065 | 1.73532 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.871558 | −0.0604317 | ||||||||
\(209\) | −0.924344 | −0.0639382 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8487 | 0.953383 | 0.476691 | − | 0.879071i | \(-0.341836\pi\) | ||||
0.476691 | + | 0.879071i | \(0.341836\pi\) | |||||||
\(212\) | 21.0578 | 1.44626 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.33759 | 0.159794 | ||||||||
\(215\) | −0.408196 | −0.0278388 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 21.5562 | 1.45997 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.586754 | −0.0395589 | ||||||||
\(221\) | 0.675180 | 0.0454175 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.4983 | 1.64053 | 0.820265 | − | 0.571984i | \(-0.193826\pi\) | ||||
0.820265 | + | 0.571984i | \(0.193826\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −30.6395 | −2.03811 | ||||||||
\(227\) | −7.73302 | −0.513258 | −0.256629 | − | 0.966510i | \(-0.582612\pi\) | ||||
−0.256629 | + | 0.966510i | \(0.582612\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.79085 | 0.316588 | 0.158294 | − | 0.987392i | \(-0.449401\pi\) | ||||
0.158294 | + | 0.987392i | \(0.449401\pi\) | |||||||
\(230\) | −2.38266 | −0.157108 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 23.4227 | 1.53777 | ||||||||
\(233\) | 9.69738 | 0.635296 | 0.317648 | − | 0.948209i | \(-0.397107\pi\) | ||||
0.317648 | + | 0.948209i | \(0.397107\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.410575 | −0.0267830 | ||||||||
\(236\) | −55.6345 | −3.62150 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.3070 | −1.50760 | −0.753802 | − | 0.657101i | \(-0.771782\pi\) | ||||
−0.753802 | + | 0.657101i | \(0.771782\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.71520 | −0.625811 | −0.312905 | − | 0.949784i | \(-0.601302\pi\) | ||||
−0.312905 | + | 0.949784i | \(0.601302\pi\) | |||||||
\(242\) | −2.52892 | −0.162565 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −26.3726 | −1.68833 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.123392 | −0.00785127 | ||||||||
\(248\) | 16.9065 | 1.07357 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.36989 | 0.213130 | ||||||||
\(251\) | −15.0400 | −0.949317 | −0.474659 | − | 0.880170i | \(-0.657428\pi\) | ||||
−0.474659 | + | 0.880170i | \(0.657428\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.05784 | −0.443722 | ||||||||
\(254\) | 22.5239 | 1.41327 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −30.7680 | −1.92300 | ||||||||
\(257\) | 15.8309 | 0.987502 | 0.493751 | − | 0.869603i | \(-0.335625\pi\) | ||||
0.493751 | + | 0.869603i | \(0.335625\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.0783269 | −0.00485763 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 39.6974 | 2.45251 | ||||||||
\(263\) | 3.07566 | 0.189653 | 0.0948265 | − | 0.995494i | \(-0.469770\pi\) | ||||
0.0948265 | + | 0.995494i | \(0.469770\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.639540 | 0.0392866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 39.2263 | 2.39613 | ||||||||
\(269\) | −10.5340 | −0.642267 | −0.321134 | − | 0.947034i | \(-0.604064\pi\) | ||||
−0.321134 | + | 0.947034i | \(0.604064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.92434 | 0.299133 | 0.149566 | − | 0.988752i | \(-0.452212\pi\) | ||||
0.149566 | + | 0.988752i | \(0.452212\pi\) | |||||||
\(272\) | −33.0222 | −2.00226 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 37.0222 | 2.23659 | ||||||||
\(275\) | 4.98218 | 0.300437 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.151312 | −0.00909146 | −0.00454573 | − | 0.999990i | \(-0.501447\pi\) | ||||
−0.00454573 | + | 0.999990i | \(0.501447\pi\) | |||||||
\(278\) | 47.1634 | 2.82867 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.51615 | −0.388721 | −0.194360 | − | 0.980930i | \(-0.562263\pi\) | ||||
−0.194360 | + | 0.980930i | \(0.562263\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.390376 | 0.0232055 | 0.0116027 | − | 0.999933i | \(-0.496307\pi\) | ||||
0.0116027 | + | 0.999933i | \(0.496307\pi\) | |||||||
\(284\) | 26.8810 | 1.59509 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.337590 | −0.0199621 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.58170 | 0.504806 | ||||||||
\(290\) | 1.30529 | 0.0766496 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −34.5767 | −2.02345 | ||||||||
\(293\) | 29.4304 | 1.71934 | 0.859671 | − | 0.510848i | \(-0.170669\pi\) | ||||
0.859671 | + | 0.510848i | \(0.170669\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.68966 | −0.0983755 | ||||||||
\(296\) | −60.4704 | −3.51477 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 30.0094 | 1.73840 | ||||||||
\(299\) | −0.942164 | −0.0544868 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 28.6395 | 1.64802 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.03497 | 0.346129 | ||||||||
\(305\) | −0.800952 | −0.0458624 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.6974 | −1.35248 | −0.676240 | − | 0.736681i | \(-0.736392\pi\) | ||||
−0.676240 | + | 0.736681i | \(0.736392\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.942164 | 0.0535113 | ||||||||
\(311\) | −12.2313 | −0.693576 | −0.346788 | − | 0.937944i | \(-0.612728\pi\) | ||||
−0.346788 | + | 0.937944i | \(0.612728\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.1735 | 1.08375 | 0.541875 | − | 0.840459i | \(-0.317714\pi\) | ||||
0.541875 | + | 0.840459i | \(0.317714\pi\) | |||||||
\(314\) | −51.5461 | −2.90891 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 62.0444 | 3.49027 | ||||||||
\(317\) | −29.5562 | −1.66004 | −0.830020 | − | 0.557734i | \(-0.811671\pi\) | ||||
−0.830020 | + | 0.557734i | \(0.811671\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.86651 | 0.216483 | ||||||||
\(320\) | −0.259263 | −0.0144933 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.67518 | −0.260134 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.665081 | 0.0368920 | ||||||||
\(326\) | 48.8258 | 2.70421 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −71.7774 | −3.96324 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.6496 | 1.02508 | 0.512538 | − | 0.858664i | \(-0.328705\pi\) | ||||
0.512538 | + | 0.858664i | \(0.328705\pi\) | |||||||
\(332\) | −5.31472 | −0.291683 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −31.9644 | −1.74901 | ||||||||
\(335\) | 1.19133 | 0.0650892 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.0222 | −1.14515 | −0.572576 | − | 0.819852i | \(-0.694056\pi\) | ||||
−0.572576 | + | 0.819852i | \(0.694056\pi\) | |||||||
\(338\) | 32.8309 | 1.78576 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.96770 | −0.160946 | ||||||||
\(341\) | 2.79085 | 0.151133 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 18.5239 | 0.998740 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 50.1957 | 2.69854 | ||||||||
\(347\) | −23.1634 | −1.24348 | −0.621738 | − | 0.783225i | \(-0.713573\pi\) | ||||
−0.621738 | + | 0.783225i | \(0.713573\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0979 | 1.50404 | 0.752022 | − | 0.659138i | \(-0.229079\pi\) | ||||
0.752022 | + | 0.659138i | \(0.229079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.39543 | 0.234277 | ||||||||
\(353\) | −33.4126 | −1.77837 | −0.889186 | − | 0.457546i | \(-0.848728\pi\) | ||||
−0.889186 | + | 0.457546i | \(0.848728\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.816393 | 0.0433296 | ||||||||
\(356\) | 68.4882 | 3.62987 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −30.3470 | −1.60389 | ||||||||
\(359\) | −13.5817 | −0.716815 | −0.358407 | − | 0.933565i | \(-0.616680\pi\) | ||||
−0.358407 | + | 0.933565i | \(0.616680\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1456 | −0.955031 | ||||||||
\(362\) | 6.76531 | 0.355577 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.05012 | −0.0549655 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.73302 | 0.194862 | 0.0974309 | − | 0.995242i | \(-0.468937\pi\) | ||||
0.0974309 | + | 0.995242i | \(0.468937\pi\) | |||||||
\(368\) | 46.0800 | 2.40209 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.36989 | −0.175192 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.94216 | 0.359452 | 0.179726 | − | 0.983717i | \(-0.442479\pi\) | ||||
0.179726 | + | 0.983717i | \(0.442479\pi\) | |||||||
\(374\) | −12.7909 | −0.661399 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.6318 | 0.960863 | ||||||||
\(377\) | 0.516148 | 0.0265830 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.390376 | −0.0200523 | −0.0100261 | − | 0.999950i | \(-0.503191\pi\) | ||||
−0.0100261 | + | 0.999950i | \(0.503191\pi\) | |||||||
\(380\) | 0.542362 | 0.0278226 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.40820 | 0.430201 | ||||||||
\(383\) | −0.533968 | −0.0272845 | −0.0136422 | − | 0.999907i | \(-0.504343\pi\) | ||||
−0.0136422 | + | 0.999907i | \(0.504343\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −46.4627 | −2.36489 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −56.2212 | −2.85420 | ||||||||
\(389\) | 10.4983 | 0.532286 | 0.266143 | − | 0.963934i | \(-0.414251\pi\) | ||||
0.266143 | + | 0.963934i | \(0.414251\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.6974 | −1.80529 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.5239 | −1.03398 | ||||||||
\(395\) | 1.88433 | 0.0948108 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.7552 | 1.04167 | 0.520837 | − | 0.853656i | \(-0.325620\pi\) | ||||
0.520837 | + | 0.853656i | \(0.325620\pi\) | |||||||
\(398\) | −16.4983 | −0.826986 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −32.5282 | −1.62641 | ||||||||
\(401\) | −21.3248 | −1.06491 | −0.532455 | − | 0.846458i | \(-0.678731\pi\) | ||||
−0.532455 | + | 0.846458i | \(0.678731\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.372556 | 0.0185583 | ||||||||
\(404\) | −42.1601 | −2.09754 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.98218 | −0.494798 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.9287 | −1.67767 | −0.838834 | − | 0.544388i | \(-0.816762\pi\) | ||||
−0.838834 | + | 0.544388i | \(0.816762\pi\) | |||||||
\(410\) | −4.00000 | −0.197546 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −43.2892 | −2.13270 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.161411 | −0.00792338 | ||||||||
\(416\) | 0.586754 | 0.0287680 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.33759 | 0.114335 | ||||||||
\(419\) | −9.99228 | −0.488155 | −0.244077 | − | 0.969756i | \(-0.578485\pi\) | ||||
−0.244077 | + | 0.969756i | \(0.578485\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.9822 | −1.46124 | −0.730621 | − | 0.682783i | \(-0.760769\pi\) | ||||
−0.730621 | + | 0.682783i | \(0.760769\pi\) | |||||||
\(422\) | −35.0222 | −1.70485 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −29.0222 | −1.40944 | ||||||||
\(425\) | 25.1990 | 1.22233 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.06289 | −0.196387 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.03230 | 0.0497817 | ||||||||
\(431\) | 2.54169 | 0.122429 | 0.0612144 | − | 0.998125i | \(-0.480503\pi\) | ||||
0.0612144 | + | 0.998125i | \(0.480503\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.3827 | −0.979528 | −0.489764 | − | 0.871855i | \(-0.662917\pi\) | ||||
−0.489764 | + | 0.871855i | \(0.662917\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −37.4660 | −1.79430 | ||||||||
\(437\) | 6.52387 | 0.312079 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.45831 | 0.260511 | 0.130256 | − | 0.991480i | \(-0.458420\pi\) | ||||
0.130256 | + | 0.991480i | \(0.458420\pi\) | |||||||
\(440\) | 0.808672 | 0.0385519 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.70748 | −0.0812163 | ||||||||
\(443\) | 10.6496 | 0.505980 | 0.252990 | − | 0.967469i | \(-0.418586\pi\) | ||||
0.252990 | + | 0.967469i | \(0.418586\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.08003 | 0.0986030 | ||||||||
\(446\) | −61.9543 | −2.93362 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.0323 | −1.27573 | −0.637866 | − | 0.770147i | \(-0.720183\pi\) | ||||
−0.637866 | + | 0.770147i | \(0.720183\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.8487 | −0.557933 | ||||||||
\(452\) | 53.2535 | 2.50484 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.5562 | 0.917816 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.79085 | 0.224107 | 0.112053 | − | 0.993702i | \(-0.464257\pi\) | ||||
0.112053 | + | 0.993702i | \(0.464257\pi\) | |||||||
\(458\) | −12.1157 | −0.566128 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.14121 | 0.193085 | ||||||||
\(461\) | 22.4983 | 1.04785 | 0.523926 | − | 0.851764i | \(-0.324467\pi\) | ||||
0.523926 | + | 0.851764i | \(0.324467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.6897 | 1.19390 | 0.596950 | − | 0.802279i | \(-0.296379\pi\) | ||||
0.596950 | + | 0.802279i | \(0.296379\pi\) | |||||||
\(464\) | −25.2441 | −1.17193 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.5239 | −1.13605 | ||||||||
\(467\) | 4.62172 | 0.213868 | 0.106934 | − | 0.994266i | \(-0.465897\pi\) | ||||
0.106934 | + | 0.994266i | \(0.465897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.03831 | 0.0478937 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 76.6762 | 3.52931 | ||||||||
\(473\) | 3.05784 | 0.140599 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.60525 | −0.211303 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 58.9415 | 2.69592 | ||||||||
\(479\) | −0.372556 | −0.0170225 | −0.00851126 | − | 0.999964i | \(-0.502709\pi\) | ||||
−0.00851126 | + | 0.999964i | \(0.502709\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.33254 | −0.0607586 | ||||||||
\(482\) | 24.5689 | 1.11908 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.39543 | 0.199792 | ||||||||
\(485\) | −1.70748 | −0.0775325 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.30262 | 0.194971 | 0.0974853 | − | 0.995237i | \(-0.468920\pi\) | ||||
0.0974853 | + | 0.995237i | \(0.468920\pi\) | |||||||
\(488\) | 36.3470 | 1.64535 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.4583 | −1.14892 | −0.574459 | − | 0.818534i | \(-0.694787\pi\) | ||||
−0.574459 | + | 0.818534i | \(0.694787\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.5562 | 0.880765 | ||||||||
\(494\) | 0.312049 | 0.0140398 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18.2212 | −0.818158 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.39038 | −0.375605 | −0.187802 | − | 0.982207i | \(-0.560136\pi\) | ||||
−0.187802 | + | 0.982207i | \(0.560136\pi\) | |||||||
\(500\) | −5.85708 | −0.261937 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 38.0350 | 1.69758 | ||||||||
\(503\) | −26.7552 | −1.19296 | −0.596478 | − | 0.802629i | \(-0.703434\pi\) | ||||
−0.596478 | + | 0.802629i | \(0.703434\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.28043 | −0.0569783 | ||||||||
\(506\) | 17.8487 | 0.793471 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −39.1480 | −1.73691 | ||||||||
\(509\) | −18.0000 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 50.4049 | 2.22760 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −40.0350 | −1.76587 | ||||||||
\(515\) | −1.31472 | −0.0579335 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.07566 | 0.135267 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.107951 | 0.00473397 | ||||||||
\(521\) | −1.44821 | −0.0634473 | −0.0317237 | − | 0.999497i | \(-0.510100\pi\) | ||||
−0.0317237 | + | 0.999497i | \(0.510100\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.5740 | −1.03082 | −0.515409 | − | 0.856944i | \(-0.672360\pi\) | ||||
−0.515409 | + | 0.856944i | \(0.672360\pi\) | |||||||
\(524\) | −68.9967 | −3.01413 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.77808 | −0.339140 | ||||||||
\(527\) | 14.1157 | 0.614888 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 26.8130 | 1.16578 | ||||||||
\(530\) | −1.61734 | −0.0702529 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.58170 | −0.0685112 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.123392 | −0.00533472 | ||||||||
\(536\) | −54.0622 | −2.33513 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.6395 | 1.14851 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.4983 | −0.795305 | −0.397653 | − | 0.917536i | \(-0.630175\pi\) | ||||
−0.397653 | + | 0.917536i | \(0.630175\pi\) | |||||||
\(542\) | −12.4533 | −0.534913 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 22.2313 | 0.953161 | ||||||||
\(545\) | −1.13787 | −0.0487409 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000 | 0.855138 | 0.427569 | − | 0.903983i | \(-0.359370\pi\) | ||||
0.427569 | + | 0.903983i | \(0.359370\pi\) | |||||||
\(548\) | −64.3470 | −2.74877 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −12.5995 | −0.537246 | ||||||||
\(551\) | −3.57398 | −0.152257 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.382656 | 0.0162575 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −81.9731 | −3.47643 | ||||||||
\(557\) | −1.98218 | −0.0839877 | −0.0419938 | − | 0.999118i | \(-0.513371\pi\) | ||||
−0.0419938 | + | 0.999118i | \(0.513371\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.408196 | 0.0172649 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.4788 | 0.695116 | ||||||||
\(563\) | 1.98990 | 0.0838643 | 0.0419322 | − | 0.999120i | \(-0.486649\pi\) | ||||
0.0419322 | + | 0.999120i | \(0.486649\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.61734 | 0.0680422 | ||||||||
\(566\) | −0.987230 | −0.0414964 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −37.0477 | −1.55449 | ||||||||
\(569\) | 14.5340 | 0.609296 | 0.304648 | − | 0.952465i | \(-0.401461\pi\) | ||||
0.304648 | + | 0.952465i | \(0.401461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.2791 | −1.22529 | −0.612646 | − | 0.790358i | \(-0.709895\pi\) | ||||
−0.612646 | + | 0.790358i | \(0.709895\pi\) | |||||||
\(572\) | 0.586754 | 0.0245334 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −35.1634 | −1.46642 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.59180 | 0.232790 | 0.116395 | − | 0.993203i | \(-0.462866\pi\) | ||||
0.116395 | + | 0.993203i | \(0.462866\pi\) | |||||||
\(578\) | −21.7024 | −0.902702 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.26869 | −0.0942022 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.79085 | −0.198417 | ||||||||
\(584\) | 47.6540 | 1.97194 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −74.4270 | −3.07455 | ||||||||
\(587\) | −2.80867 | −0.115926 | −0.0579632 | − | 0.998319i | \(-0.518461\pi\) | ||||
−0.0579632 | + | 0.998319i | \(0.518461\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.57971 | −0.106295 | ||||||||
\(590\) | 4.27300 | 0.175917 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 65.1728 | 2.67859 | ||||||||
\(593\) | −42.1957 | −1.73277 | −0.866385 | − | 0.499377i | \(-0.833562\pi\) | ||||
−0.866385 | + | 0.499377i | \(0.833562\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −52.1584 | −2.13649 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.38266 | 0.0974340 | ||||||||
\(599\) | −34.3470 | −1.40338 | −0.701691 | − | 0.712482i | \(-0.747571\pi\) | ||||
−0.701691 | + | 0.712482i | \(0.747571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.98218 | −0.244018 | −0.122009 | − | 0.992529i | \(-0.538934\pi\) | ||||
−0.122009 | + | 0.992529i | \(0.538934\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −49.7774 | −2.02541 | ||||||||
\(605\) | 0.133492 | 0.00542722 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.12339 | −0.329718 | −0.164859 | − | 0.986317i | \(-0.552717\pi\) | ||||
−0.164859 | + | 0.986317i | \(0.552717\pi\) | |||||||
\(608\) | −4.06289 | −0.164772 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.02554 | 0.0820117 | ||||||||
\(611\) | 0.410575 | 0.0166101 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.5239 | −0.667393 | −0.333696 | − | 0.942681i | \(-0.608296\pi\) | ||||
−0.333696 | + | 0.942681i | \(0.608296\pi\) | |||||||
\(614\) | 59.9287 | 2.41853 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.8843 | −0.478445 | −0.239223 | − | 0.970965i | \(-0.576893\pi\) | ||||
−0.239223 | + | 0.970965i | \(0.576893\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.0222 | −1.72921 | −0.864604 | − | 0.502454i | \(-0.832431\pi\) | ||||
−0.864604 | + | 0.502454i | \(0.832431\pi\) | |||||||
\(620\) | −1.63754 | −0.0657653 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30.9321 | 1.24026 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7330 | 0.989321 | ||||||||
\(626\) | −48.4882 | −1.93798 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 89.5905 | 3.57505 | ||||||||
\(629\) | −50.4882 | −2.01310 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.5817 | 0.540679 | 0.270340 | − | 0.962765i | \(-0.412864\pi\) | ||||
0.270340 | + | 0.962765i | \(0.412864\pi\) | |||||||
\(632\) | −85.5104 | −3.40142 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 74.7451 | 2.96851 | ||||||||
\(635\) | −1.18895 | −0.0471820 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9.77808 | −0.387118 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.82916 | 0.0723040 | ||||||||
\(641\) | −36.7552 | −1.45174 | −0.725872 | − | 0.687830i | \(-0.758563\pi\) | ||||
−0.725872 | + | 0.687830i | \(0.758563\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.3369 | 1.74848 | 0.874239 | − | 0.485496i | \(-0.161361\pi\) | ||||
0.874239 | + | 0.485496i | \(0.161361\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.8231 | 0.465176 | ||||||||
\(647\) | −17.9721 | −0.706555 | −0.353278 | − | 0.935519i | \(-0.614933\pi\) | ||||
−0.353278 | + | 0.935519i | \(0.614933\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.6574 | 0.496845 | ||||||||
\(650\) | −1.68193 | −0.0659709 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −84.8625 | −3.32347 | ||||||||
\(653\) | 22.1957 | 0.868585 | 0.434292 | − | 0.900772i | \(-0.356998\pi\) | ||||
0.434292 | + | 0.900772i | \(0.356998\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.09547 | −0.0818769 | ||||||||
\(656\) | 77.3591 | 3.02037 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.99228 | −0.389244 | −0.194622 | − | 0.980878i | \(-0.562348\pi\) | ||||
−0.194622 | + | 0.980878i | \(0.562348\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.9543 | −1.08729 | −0.543647 | − | 0.839314i | \(-0.682957\pi\) | ||||
−0.543647 | + | 0.839314i | \(0.682957\pi\) | |||||||
\(662\) | −47.1634 | −1.83306 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.32482 | 0.284258 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27.2892 | −1.05664 | ||||||||
\(668\) | 55.5562 | 2.14953 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.01277 | −0.116393 | ||||||||
\(671\) | 6.00000 | 0.231627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.4203 | −1.67373 | −0.836865 | − | 0.547410i | \(-0.815614\pi\) | ||||
−0.836865 | + | 0.547410i | \(0.815614\pi\) | |||||||
\(674\) | 53.1634 | 2.04778 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −57.0622 | −2.19470 | ||||||||
\(677\) | −12.3470 | −0.474534 | −0.237267 | − | 0.971444i | \(-0.576252\pi\) | ||||
−0.237267 | + | 0.971444i | \(0.576252\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.09013 | 0.156849 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.05784 | −0.270259 | ||||||||
\(683\) | 27.8386 | 1.06521 | 0.532607 | − | 0.846363i | \(-0.321212\pi\) | ||||
0.532607 | + | 0.846363i | \(0.321212\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.95426 | −0.0746684 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −19.9644 | −0.761134 | ||||||||
\(689\) | −0.639540 | −0.0243645 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.8010 | 0.639138 | 0.319569 | − | 0.947563i | \(-0.396462\pi\) | ||||
0.319569 | + | 0.947563i | \(0.396462\pi\) | |||||||
\(692\) | −87.2434 | −3.31650 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 58.5784 | 2.22360 | ||||||||
\(695\) | −2.48958 | −0.0944350 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −59.9287 | −2.26996 | ||||||||
\(698\) | −71.0572 | −2.68955 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.16341 | −0.346097 | −0.173049 | − | 0.984913i | \(-0.555362\pi\) | ||||
−0.173049 | + | 0.984913i | \(0.555362\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.22697 | 0.348002 | ||||||||
\(704\) | 1.94216 | 0.0731981 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 84.4977 | 3.18011 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.7475 | −1.30497 | −0.652485 | − | 0.757802i | \(-0.726273\pi\) | ||||
−0.652485 | + | 0.757802i | \(0.726273\pi\) | |||||||
\(710\) | −2.06459 | −0.0774827 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −94.3914 | −3.53747 | ||||||||
\(713\) | −19.6974 | −0.737673 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0178201 | 0.000666434 0 | ||||||||
\(716\) | 52.7451 | 1.97118 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 34.3470 | 1.28182 | ||||||||
\(719\) | −25.1557 | −0.938149 | −0.469074 | − | 0.883159i | \(-0.655412\pi\) | ||||
−0.469074 | + | 0.883159i | \(0.655412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 45.8887 | 1.70780 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.7586 | −0.437003 | ||||||||
\(725\) | 19.2636 | 0.715434 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.5918 | 0.874972 | 0.437486 | − | 0.899225i | \(-0.355869\pi\) | ||||
0.437486 | + | 0.899225i | \(0.355869\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.65566 | 0.0982902 | ||||||||
\(731\) | 15.4660 | 0.572032 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.9287 | −0.809956 | −0.404978 | − | 0.914326i | \(-0.632721\pi\) | ||||
−0.404978 | + | 0.914326i | \(0.632721\pi\) | |||||||
\(734\) | −9.44049 | −0.348455 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −31.0222 | −1.14349 | ||||||||
\(737\) | −8.92434 | −0.328732 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.0578 | 1.28962 | 0.644812 | − | 0.764341i | \(-0.276936\pi\) | ||||
0.644812 | + | 0.764341i | \(0.276936\pi\) | |||||||
\(740\) | 5.85708 | 0.215311 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.3070 | 1.14854 | 0.574271 | − | 0.818665i | \(-0.305285\pi\) | ||||
0.574271 | + | 0.818665i | \(0.305285\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.58408 | −0.0580363 | ||||||||
\(746\) | −17.5562 | −0.642777 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 22.2313 | 0.812858 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.42602 | −0.161508 | −0.0807538 | − | 0.996734i | \(-0.525733\pi\) | ||||
−0.0807538 | + | 0.996734i | \(0.525733\pi\) | |||||||
\(752\) | −20.0807 | −0.732268 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.30529 | −0.0475360 | ||||||||
\(755\) | −1.51177 | −0.0550190 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.51615 | 0.0914509 | 0.0457255 | − | 0.998954i | \(-0.485440\pi\) | ||||
0.0457255 | + | 0.998954i | \(0.485440\pi\) | |||||||
\(758\) | 0.987230 | 0.0358578 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.747491 | −0.0271144 | ||||||||
\(761\) | 13.7330 | 0.497821 | 0.248911 | − | 0.968526i | \(-0.419927\pi\) | ||||
0.248911 | + | 0.968526i | \(0.419927\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −14.6140 | −0.528716 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.35036 | 0.0487905 | ||||||||
\(767\) | 1.68966 | 0.0610099 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.4805 | −1.67613 | −0.838065 | − | 0.545570i | \(-0.816313\pi\) | ||||
−0.838065 | + | 0.545570i | \(0.816313\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 80.7552 | 2.90644 | ||||||||
\(773\) | −45.9822 | −1.65386 | −0.826932 | − | 0.562302i | \(-0.809916\pi\) | ||||
−0.826932 | + | 0.562302i | \(0.809916\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.9045 | 0.499465 | ||||||||
\(776\) | 77.4849 | 2.78155 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.5494 | −0.951842 | ||||||||
\(779\) | 10.9523 | 0.392406 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.11567 | −0.218836 | ||||||||
\(782\) | 90.2757 | 3.22825 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.72092 | 0.0971138 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.9243 | −1.45880 | −0.729398 | − | 0.684090i | \(-0.760200\pi\) | ||||
−0.729398 | + | 0.684090i | \(0.760200\pi\) | |||||||
\(788\) | 35.6718 | 1.27076 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.76531 | −0.169542 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.800952 | 0.0284426 | ||||||||
\(794\) | −52.4882 | −1.86274 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 28.6752 | 1.01636 | ||||||||
\(797\) | −28.8786 | −1.02293 | −0.511466 | − | 0.859303i | \(-0.670898\pi\) | ||||
−0.511466 | + | 0.859303i | \(0.670898\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.5562 | 0.550338 | ||||||||
\(800\) | 21.8988 | 0.774240 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 53.9287 | 1.90429 | ||||||||
\(803\) | 7.86651 | 0.277603 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.942164 | −0.0331863 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 58.1056 | 2.04415 | ||||||||
\(809\) | −6.51615 | −0.229096 | −0.114548 | − | 0.993418i | \(-0.536542\pi\) | ||||
−0.114548 | + | 0.993418i | \(0.536542\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.5060 | −1.35213 | −0.676065 | − | 0.736842i | \(-0.736316\pi\) | ||||
−0.676065 | + | 0.736842i | \(0.736316\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 25.2441 | 0.884806 | ||||||||
\(815\) | −2.57733 | −0.0902799 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.82649 | −0.0988864 | ||||||||
\(818\) | 85.8029 | 3.00003 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.95226 | 0.242784 | ||||||||
\(821\) | 37.3769 | 1.30446 | 0.652232 | − | 0.758019i | \(-0.273833\pi\) | ||||
0.652232 | + | 0.758019i | \(0.273833\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.0400 | 1.50028 | 0.750140 | − | 0.661279i | \(-0.229986\pi\) | ||||
0.750140 | + | 0.661279i | \(0.229986\pi\) | |||||||
\(824\) | 59.6617 | 2.07842 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.3426 | −0.394422 | −0.197211 | − | 0.980361i | \(-0.563188\pi\) | ||||
−0.197211 | + | 0.980361i | \(0.563188\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.4983 | −0.503548 | −0.251774 | − | 0.967786i | \(-0.581014\pi\) | ||||
−0.251774 | + | 0.967786i | \(0.581014\pi\) | |||||||
\(830\) | 0.408196 | 0.0141687 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.259263 | 0.00898833 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.68728 | 0.0583906 | ||||||||
\(836\) | −4.06289 | −0.140518 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.2697 | 0.872926 | ||||||||
\(839\) | −3.60962 | −0.124618 | −0.0623090 | − | 0.998057i | \(-0.519846\pi\) | ||||
−0.0623090 | + | 0.998057i | \(0.519846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0501 | −0.484487 | ||||||||
\(842\) | 75.8225 | 2.61301 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 60.8709 | 2.09526 | ||||||||
\(845\) | −1.73302 | −0.0596176 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 31.2791 | 1.07413 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −63.7263 | −2.18579 | ||||||||
\(851\) | 70.4526 | 2.41508 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.6496 | 0.843988 | 0.421994 | − | 0.906599i | \(-0.361330\pi\) | ||||
0.421994 | + | 0.906599i | \(0.361330\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.59952 | 0.191388 | ||||||||
\(857\) | 17.9287 | 0.612433 | 0.306217 | − | 0.951962i | \(-0.400937\pi\) | ||||
0.306217 | + | 0.951962i | \(0.400937\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.6974 | 0.535588 | 0.267794 | − | 0.963476i | \(-0.413705\pi\) | ||||
0.267794 | + | 0.963476i | \(0.413705\pi\) | |||||||
\(860\) | −1.79420 | −0.0611816 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.42772 | −0.218929 | ||||||||
\(863\) | 15.0578 | 0.512575 | 0.256287 | − | 0.966601i | \(-0.417501\pi\) | ||||
0.256287 | + | 0.966601i | \(0.417501\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.64964 | −0.0900904 | ||||||||
\(866\) | 51.5461 | 1.75161 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.1157 | −0.478841 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.19133 | −0.0403666 | ||||||||
\(872\) | 51.6362 | 1.74862 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16.4983 | −0.558064 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.8487 | −1.48066 | −0.740332 | − | 0.672241i | \(-0.765332\pi\) | ||||
−0.740332 | + | 0.672241i | \(0.765332\pi\) | |||||||
\(878\) | −13.8036 | −0.465850 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.871558 | −0.0293802 | ||||||||
\(881\) | 11.0656 | 0.372808 | 0.186404 | − | 0.982473i | \(-0.440317\pi\) | ||||
0.186404 | + | 0.982473i | \(0.440317\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.72530 | 0.192672 | 0.0963358 | − | 0.995349i | \(-0.469288\pi\) | ||||
0.0963358 | + | 0.995349i | \(0.469288\pi\) | |||||||
\(884\) | 2.96770 | 0.0998147 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.9321 | −0.904800 | ||||||||
\(887\) | 15.0935 | 0.506789 | 0.253395 | − | 0.967363i | \(-0.418453\pi\) | ||||
0.253395 | + | 0.967363i | \(0.418453\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5.26023 | −0.176323 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 107.681 | 3.60541 | ||||||||
\(893\) | −2.84296 | −0.0951362 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.60190 | 0.0535457 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 68.3625 | 2.28128 | ||||||||
\(899\) | 10.7909 | 0.359895 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.2313 | −0.807263 | ||||||||
\(902\) | 29.9644 | 0.997704 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −73.3948 | −2.44107 | ||||||||
\(905\) | −0.357115 | −0.0118709 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.2993 | 1.37132 | 0.685660 | − | 0.727922i | \(-0.259514\pi\) | ||||
0.685660 | + | 0.727922i | \(0.259514\pi\) | |||||||
\(908\) | −33.9899 | −1.12799 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.45059 | −0.114323 | −0.0571616 | − | 0.998365i | \(-0.518205\pi\) | ||||
−0.0571616 | + | 0.998365i | \(0.518205\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.20915 | 0.0400170 | ||||||||
\(914\) | −12.1157 | −0.400751 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.0578 | 0.695770 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.8265 | −0.357133 | −0.178567 | − | 0.983928i | \(-0.557146\pi\) | ||||
−0.178567 | + | 0.983928i | \(0.557146\pi\) | |||||||
\(920\) | −5.70748 | −0.188170 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −56.8964 | −1.87378 | ||||||||
\(923\) | −0.816393 | −0.0268719 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −49.7330 | −1.63521 | ||||||||
\(926\) | −64.9670 | −2.13495 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.9950 | 0.557887 | ||||||||
\(929\) | 17.4684 | 0.573120 | 0.286560 | − | 0.958062i | \(-0.407488\pi\) | ||||
0.286560 | + | 0.958062i | \(0.407488\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 42.6241 | 1.39620 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.6880 | −0.382441 | ||||||||
\(935\) | 0.675180 | 0.0220808 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.5340 | −0.344130 | −0.172065 | − | 0.985086i | \(-0.555044\pi\) | ||||
−0.172065 | + | 0.985086i | \(0.555044\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.80465 | −0.0588613 | ||||||||
\(941\) | −16.1513 | −0.526518 | −0.263259 | − | 0.964725i | \(-0.584797\pi\) | ||||
−0.263259 | + | 0.964725i | \(0.584797\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 83.6261 | 2.72324 | ||||||||
\(944\) | −82.6389 | −2.68967 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.73302 | −0.251422 | ||||||||
\(947\) | 6.91662 | 0.224760 | 0.112380 | − | 0.993665i | \(-0.464153\pi\) | ||||
0.112380 | + | 0.993665i | \(0.464153\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.05012 | 0.0340882 | ||||||||
\(950\) | 11.6463 | 0.377856 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.1335 | 0.522615 | 0.261308 | − | 0.965256i | \(-0.415846\pi\) | ||||
0.261308 | + | 0.965256i | \(0.415846\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.443837 | −0.0143622 | ||||||||
\(956\) | −102.444 | −3.31328 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.942164 | 0.0304399 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.2111 | −0.748747 | ||||||||
\(962\) | 3.36989 | 0.108649 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −42.7024 | −1.37535 | ||||||||
\(965\) | 2.45259 | 0.0789516 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.8487 | 0.573975 | 0.286988 | − | 0.957934i | \(-0.407346\pi\) | ||||
0.286988 | + | 0.957934i | \(0.407346\pi\) | |||||||
\(968\) | −6.05784 | −0.194706 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.31807 | 0.138645 | ||||||||
\(971\) | 33.9566 | 1.08972 | 0.544860 | − | 0.838527i | \(-0.316583\pi\) | ||||
0.544860 | + | 0.838527i | \(0.316583\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.8810 | −0.348649 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −39.1735 | −1.25391 | ||||||||
\(977\) | −41.0222 | −1.31242 | −0.656208 | − | 0.754580i | \(-0.727841\pi\) | ||||
−0.656208 | + | 0.754580i | \(0.727841\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.5817 | −0.497993 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 64.3820 | 2.05451 | ||||||||
\(983\) | 42.3470 | 1.35066 | 0.675330 | − | 0.737516i | \(-0.264001\pi\) | ||||
0.675330 | + | 0.737516i | \(0.264001\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.08338 | 0.0345192 | ||||||||
\(986\) | −49.4559 | −1.57500 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.542362 | −0.0172548 | ||||||||
\(989\) | −21.5817 | −0.686258 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.9687 | 1.61908 | 0.809538 | − | 0.587068i | \(-0.199718\pi\) | ||||
0.809538 | + | 0.587068i | \(0.199718\pi\) | |||||||
\(992\) | 12.2670 | 0.389477 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.870884 | 0.0276089 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.8608 | 1.04071 | 0.520356 | − | 0.853950i | \(-0.325799\pi\) | ||||
0.520356 | + | 0.853950i | \(0.325799\pi\) | |||||||
\(998\) | 21.2186 | 0.671662 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4851.2.a.bp.1.1 | 3 | ||
3.2 | odd | 2 | 1617.2.a.s.1.3 | 3 | |||
7.6 | odd | 2 | 693.2.a.m.1.1 | 3 | |||
21.20 | even | 2 | 231.2.a.d.1.3 | ✓ | 3 | ||
77.76 | even | 2 | 7623.2.a.cb.1.3 | 3 | |||
84.83 | odd | 2 | 3696.2.a.bp.1.2 | 3 | |||
105.104 | even | 2 | 5775.2.a.bw.1.1 | 3 | |||
231.230 | odd | 2 | 2541.2.a.bi.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.a.d.1.3 | ✓ | 3 | 21.20 | even | 2 | ||
693.2.a.m.1.1 | 3 | 7.6 | odd | 2 | |||
1617.2.a.s.1.3 | 3 | 3.2 | odd | 2 | |||
2541.2.a.bi.1.1 | 3 | 231.230 | odd | 2 | |||
3696.2.a.bp.1.2 | 3 | 84.83 | odd | 2 | |||
4851.2.a.bp.1.1 | 3 | 1.1 | even | 1 | trivial | ||
5775.2.a.bw.1.1 | 3 | 105.104 | even | 2 | |||
7623.2.a.cb.1.3 | 3 | 77.76 | even | 2 |